Finite Group Databasebeta

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C₁₉×Dic₄₇₇ #49136208

order	36252
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×Dic₄₇₇
unambiguous semidirect product	C₉⋊(C₁₉×Dic₅₃)

Splittings

derived, Hall	C₉×C₅₃ ⋊ C₄×C₁₉
Hall	C₉×C₁₉×C₅₃ ⋊ C₄
Hall	C₁₉×C₅₃ ⋊ Dic₉
Hall	C₉×C₁₉ ⋊ Dic₅₃
Sylow	C₅₃ ⋊ C₁₉×Dic₉
Sylow	C₉ ⋊ C₁₉×Dic₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₄₇₇
commutator, hypocenter	C₉×C₅₃	C₄×C₁₉
Frattini	C₂×C₃	C₁₉×D₁₅₉
Fitting	C₂×C₉×C₁₉×C₅₃	C₂
socle, prime radical	C₂×C₃×C₁₉×C₅₃	D₃
cosocle	C₂×C₉×C₅₃	C₂×C₁₉
LCS	G ▷ C₉×C₅₃
UCS	C₁ ◁ C₂×C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 36252

Conjugacy classes & character table

9120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 7);